This discussion has become unwieldy and unproductive, but there are two things worth to comment here.

For me it is more basic: acknowledging the existence of God. The rest is secondary.

From my viewpoint, this notion is a common ignorance among monotheists. You use the word "God" as if its meaning were something singular and self-explanatory, but it is actually laden with unspoken assumptions about what "God" means, a lack of recognition that there are several different and incompatible "Gods" if one looks at the beliefs of different people (compare, say, the Prime Mover God of an Enlightement philosopher to the talkative personal God of an Irish drunkard), not to mention religions that have no God but multiple small-case gods. People's religious outlook is most certainly not a dichotomy, there are literally millions of different views on the existence of gods.

I am curious: why was it important for your parents to pretend religion?

Because, like eurogreen's parents, my parents never told my grandparents about their apostasy, and didn't want me to blow their cover. It was also part of keeping that cover up that we didn't opt out of religion class at school when in West Germany (an experience which felt much less oppressive for me, BTW, than prayer before sleep and Sunday church when on holiday with my grandparents).

The reason my parents didn't tell about their apostasy is that they feared my grandparents (three Catholics, one of them converted from a Lutheran as a youth along with family, and a Calvinist) would both get emotionally distressed and angrily start to keep a distance, things that happened in other families. Both of those reactions are the consequences of the coercive nature of religious instruction: in their traditional way of religion, you are made to feel guilt for any omission of religious practice, and a child's apostasy is the child's moral failure and eternal damnation and the parent's failure at education.

(Actually, my grandmother was aware that my mother doesn't go to church every Sunday, but she suppressed suspicions by believing that it's because my mother has no time besides her job and home chores. Still, a few years before her death, her suspicions about us must have solidified, as once she levelled a cryptic accusation of "apostasy" at me.)

And, again, if you didn't have experience with such religious instruction, you were the lucky exemption.

_{*Lunatic*, n.
One whose delusions are out of fashion.}